Question: Given that 10 is the arithmetic mean of the set $\{6, 13, 18, 4, x\}$, what is the value of $x$?
Answer: There are 5 numbers in this set, so we have  \begin{align*}
\frac{6+13+18+4+x}{5}&=10 \\
6+13+18+4+x&=50 \\
6+4+13+18+x&=50 \\
10+31+x &=50 \\
41+x&=50 \\
x &= \boxed{9}
\end{align*}